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          头歌C语言实验 练习6：循环结构II
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        <h2 id="第1关分数序列和"><a class="markdownIt-Anchor" href="#第1关分数序列和"></a> 第1关：分数序列和</h2>
<p>问题描述<br />
有一个分数序列2/1，3/2，5/3，8/5，13/8，21/13，…… ，求这个分数序列的前n项之和。</p>
<p>输入<br />
输入只有一个非负整数n（0≤n≤500）。</p>
<p>输出<br />
按照“分数序列前x项之和为：y”的格式输出前n项的和，其中x为项数n，y是前n项之和，保留4位小数，冒号是中文的冒号。</p>
<p>输入示例<br />
99</p>
<p>输出示例<br />
分数序列前99项之和为：160.4849</p>
<p>提示<br />
为避免溢出错误，在程序中的中间变量尽可能都使用double类型。</p>
<figure class="highlight c"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;stdio.h&gt;</span></span></span><br><span class="line"><span class="type">int</span> <span class="title function_">main</span><span class="params">()</span>&#123;</span><br><span class="line">    <span class="type">int</span> i,n;</span><br><span class="line">    <span class="type">double</span> sum=<span class="number">0</span>;</span><br><span class="line">    <span class="type">double</span> a=<span class="number">2</span>,b=<span class="number">1</span>;</span><br><span class="line">    <span class="built_in">scanf</span>(<span class="string">&quot;%d&quot;</span>,&amp;n);</span><br><span class="line">    <span class="keyword">if</span>(n!=<span class="number">0</span>)&#123;</span><br><span class="line">        sum=a/b;</span><br><span class="line">        <span class="keyword">if</span>(n&gt;=<span class="number">2</span>)&#123;</span><br><span class="line">            <span class="keyword">for</span>(i=<span class="number">1</span>;i&lt;n;i++)&#123;</span><br><span class="line">                a=a+b;</span><br><span class="line">                b=a-b;</span><br><span class="line">                sum+=a/b;</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="built_in">printf</span>(<span class="string">&quot;分数序列前%d项之和为：%.4lf&quot;</span>,n,sum);</span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<h2 id="第2关奖金发放"><a class="markdownIt-Anchor" href="#第2关奖金发放"></a> 第2关：奖金发放</h2>
<p>问题描述<br />
企业每个月发放的奖金根据当月利润进行提成。利润I低于或等于10万元（I≤100000）时，奖金可提10％；利润高于10万元，低于20万元（100000＜I≤200000）时，低于10万元的部分按10％提成，高于10万元的部分，可提成7.5％；200000＜I≤400000时，低于20万元的部分仍按上述办法提成（下同）。高于20万的部分按5％提成；400000＜I≤600000时，高于40万元的部分按3％提成；600000＜I≤1000000时，高于60万元的部分按1.5％提成；I＞1000000时，超过100万元的部分按1％提成。<br />
聪明的你能编写一段程序，根据一年中每个月的利润，计算并输出这一年内的应发奖金总额吗？</p>
<p>输入<br />
输入数据一共有12行，每一行都是一个正整数，其中第i（1≤i≤12）行的整数表示第i个月的利润（以元为单位），其中每个整数都不超过2000000。</p>
<p>输出<br />
输出只有一行，即该企业在这一年内应该发放的奖金总额（以元为单位），要求精确到小数点后两位。</p>
<p>输入示例<br />
400000<br />
106000<br />
50000<br />
580000<br />
620000<br />
1030000<br />
1700000<br />
122000<br />
640000<br />
76000<br />
60000<br />
540000</p>
<p>输出示例<br />
287000.00</p>
<p>提示<br />
为保证数据精度准确无误，涉及到实数的变量请使用double类型。<br />
输入示例中，针对每个月的利润，对应每月计算的奖金是：<br />
27500.00<br />
10450.00<br />
5000.00<br />
32900.00<br />
33800.00<br />
39800.00<br />
46500.00<br />
11650.00<br />
34100.00<br />
7600.00<br />
6000.00<br />
31700.00</p>
<figure class="highlight c"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;stdio.h&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;math.h&gt;</span></span></span><br><span class="line"><span class="type">double</span> <span class="title function_">sum</span><span class="params">(<span class="type">double</span> n)</span>&#123;</span><br><span class="line">    <span class="type">double</span> t;</span><br><span class="line">    <span class="keyword">if</span>(n/<span class="built_in">pow</span>(<span class="number">10</span>,<span class="number">4</span>)&lt;=<span class="number">10</span>)&#123;</span><br><span class="line">        <span class="keyword">return</span> n*<span class="number">0.1</span>;</span><br><span class="line">    &#125;<span class="keyword">else</span> <span class="keyword">if</span>(n/<span class="built_in">pow</span>(<span class="number">10</span>,<span class="number">4</span>)&lt;=<span class="number">20</span>)&#123;</span><br><span class="line">        t=sum(<span class="built_in">pow</span>(<span class="number">10</span>,<span class="number">5</span>));</span><br><span class="line">        <span class="keyword">return</span> t+(n-<span class="built_in">pow</span>(<span class="number">10</span>,<span class="number">5</span>))*<span class="number">0.075</span>;</span><br><span class="line">    &#125;<span class="keyword">else</span> <span class="keyword">if</span>(n/<span class="built_in">pow</span>(<span class="number">10</span>,<span class="number">4</span>)&lt;=<span class="number">40</span>)&#123;</span><br><span class="line">        t=sum(<span class="number">2</span>*<span class="built_in">pow</span>(<span class="number">10</span>,<span class="number">5</span>));</span><br><span class="line">        <span class="keyword">return</span> t+(n<span class="number">-2</span>*<span class="built_in">pow</span>(<span class="number">10</span>,<span class="number">5</span>))*<span class="number">0.05</span>;</span><br><span class="line">    &#125;<span class="keyword">else</span> <span class="keyword">if</span>(n/<span class="built_in">pow</span>(<span class="number">10</span>,<span class="number">4</span>)&lt;=<span class="number">60</span>)&#123;</span><br><span class="line">        t=sum(<span class="number">4</span>*<span class="built_in">pow</span>(<span class="number">10</span>,<span class="number">5</span>));</span><br><span class="line">        <span class="keyword">return</span> t+(n<span class="number">-4</span>*<span class="built_in">pow</span>(<span class="number">10</span>,<span class="number">5</span>))*<span class="number">0.03</span>;</span><br><span class="line">    &#125;<span class="keyword">else</span> <span class="keyword">if</span>(n/<span class="built_in">pow</span>(<span class="number">10</span>,<span class="number">4</span>)&lt;=<span class="number">100</span>)&#123;</span><br><span class="line">        t=sum(<span class="number">6</span>*<span class="built_in">pow</span>(<span class="number">10</span>,<span class="number">5</span>));</span><br><span class="line">        <span class="keyword">return</span> t+(n<span class="number">-6</span>*<span class="built_in">pow</span>(<span class="number">10</span>,<span class="number">5</span>))*<span class="number">0.015</span>;</span><br><span class="line">    &#125;<span class="keyword">else</span>&#123;</span><br><span class="line">        t=sum(<span class="number">10</span>*<span class="built_in">pow</span>(<span class="number">10</span>,<span class="number">5</span>));</span><br><span class="line">        <span class="keyword">return</span> t+(n<span class="number">-10</span>*<span class="built_in">pow</span>(<span class="number">10</span>,<span class="number">5</span>))*<span class="number">0.01</span>;</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br><span class="line"><span class="type">int</span> <span class="title function_">main</span><span class="params">()</span>&#123;</span><br><span class="line">    <span class="type">int</span> i;</span><br><span class="line">    <span class="type">double</span> l[<span class="number">12</span>];</span><br><span class="line">    <span class="type">double</span> money=<span class="number">0</span>;</span><br><span class="line">    <span class="keyword">for</span>(i=<span class="number">0</span>;i&lt;<span class="number">12</span>;i++)&#123;</span><br><span class="line">        <span class="built_in">scanf</span>(<span class="string">&quot;%lf&quot;</span>,&amp;l[i]);</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="keyword">for</span>(i=<span class="number">0</span>;i&lt;<span class="number">12</span>;i++)&#123;</span><br><span class="line">        money+=sum(l[i]);</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="built_in">printf</span>(<span class="string">&quot;%.2lf&quot;</span>,money);</span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<h2 id="第3关成绩统计-ii"><a class="markdownIt-Anchor" href="#第3关成绩统计-ii"></a> 第3关：成绩统计 II</h2>
<p>问题描述<br />
输入若干个百分制成绩，直到输入负数时为止。<br />
请编写一段程序，统计出这些成绩的平均成绩和其中的不及格人数。</p>
<p>输入<br />
若干个用空格分开的浮点数，最后是一个负数。除最后的负数外，之前的每个浮点数代表一个百分制成绩。</p>
<p>输出<br />
输出共包括两行：<br />
第一行输出全班同学的平均成绩，保留2位小数；<br />
第二行输出不及格人数。<br />
输出格式参照输出示例，注意其中的冒号是中文冒号。</p>
<p>输入示例<br />
85.6 83.47 45.8 96.3 100 37.4 68.9 96.6 88 84.6 94.7 78.8 -2.3</p>
<p>输出示例<br />
平均成绩：80.01分<br />
不及格人数：2人</p>
<figure class="highlight c"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;stdio.h&gt;</span></span></span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="title function_">main</span><span class="params">()</span>&#123;</span><br><span class="line">    <span class="type">int</span> i=<span class="number">0</span>,n=<span class="number">0</span>;</span><br><span class="line">    <span class="type">double</span> score,avg=<span class="number">0</span>;</span><br><span class="line">    <span class="keyword">do</span>&#123;</span><br><span class="line">        <span class="built_in">scanf</span>(<span class="string">&quot;%lf&quot;</span>,&amp;score);</span><br><span class="line">        <span class="keyword">if</span>(score&lt;<span class="number">0</span>)</span><br><span class="line">            <span class="keyword">break</span>;</span><br><span class="line">        n++;</span><br><span class="line">        avg+=score;</span><br><span class="line">        <span class="keyword">if</span>(score&lt;<span class="number">60</span>)</span><br><span class="line">            i++;</span><br><span class="line">    &#125;<span class="keyword">while</span>(<span class="number">1</span>);</span><br><span class="line">    avg/=n;</span><br><span class="line">    <span class="built_in">printf</span>(<span class="string">&quot;平均成绩：%.2lf分\n不及格人数：%d人&quot;</span>,avg,i);</span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<h2 id="第4关计算圆周率-i"><a class="markdownIt-Anchor" href="#第4关计算圆周率-i"></a> 第4关：计算圆周率 I</h2>
<p>问题描述<br />
众所周知，可以使用级数展开公式近似计算圆周率π，下面的这个公式可以算是其中最简单的一个：<br />
π/4=1-1/3+1/5-1/7+1/9-…<br />
根据给定的正整数 n 使用上述公式通过计算前n项的和，近似计算圆周率π的值。</p>
<p>输入<br />
一个正整数n。</p>
<p>输出<br />
一个浮点数，表示圆周率π的近似值，精确到小数点后8位。</p>
<p>输入示例<br />
5</p>
<p>输出示例<br />
3.33968254</p>
<p>提示<br />
为保证数据精度准确无误，涉及到实数的变量请使用double类型。</p>
<figure class="highlight c"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;stdio.h&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;math.h&gt;</span></span></span><br><span class="line"></span><br><span class="line"><span class="type">int</span> <span class="title function_">main</span><span class="params">()</span>&#123;</span><br><span class="line">    <span class="type">int</span> i,n;</span><br><span class="line">    <span class="type">double</span> pi=<span class="number">0</span>;</span><br><span class="line">    <span class="built_in">scanf</span>(<span class="string">&quot;%d&quot;</span>,&amp;n);</span><br><span class="line">    <span class="keyword">for</span>(i=<span class="number">0</span>;i&lt;n;i++)&#123;</span><br><span class="line">        pi+=<span class="number">4</span>*(<span class="number">1</span>/(<span class="number">2.0</span>*(i+<span class="number">1</span>)<span class="number">-1</span>))*<span class="built_in">pow</span>(<span class="number">-1</span>,i);</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="built_in">printf</span>(<span class="string">&quot;%.8lf&quot;</span>,pi);</span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<h2 id="第5关最大公约数和最小公倍数"><a class="markdownIt-Anchor" href="#第5关最大公约数和最小公倍数"></a> 第5关：最大公约数和最小公倍数</h2>
<p>问题描述<br />
最大公约数<br />
也称为最大公因数或最大公因子，指两个或多个整数共有约数中最大的一个。<br />
求最大公约数的方法有很多，现列举最常用的两种方法。</p>
<p>辗转相除法 设有两整数 a 和 b ，则计算步骤如下：<br />
①    计算a和b的余数c；<br />
②    若c为0，则b即为两数的最大公约数；<br />
③    若c不为0，则令a = b，b = c，再重复执行步骤①。<br />
例如：求27和15的最大公约数过程为：<br />
求27和15的余数为12<br />
求15和12的余数为3<br />
求12和3的余数为0<br />
因此，3即为27和15的最大公约数。<br />
2.    相减法<br />
设有两整数 a 和 b ，则计算步骤如下：<br />
①    若a大于b，则令a = a - b；<br />
②    若a小于b，则令b = b - a；<br />
③    若a与b相等，则a（或b）即为两数的最大公约数；<br />
④    若a与b不相等，则重复执行步骤 ①。<br />
例如：求27和15的最大公约数过程为：<br />
（27 &gt; 15）27 - 15 = 12<br />
（12 &lt; 15）15 - 12 = 3<br />
（12 &gt; 3）12 - 3 = 9<br />
（9 &gt; 3）9 - 3 = 6<br />
（6 &gt; 3）6 – 3 = 3<br />
因为a和b的值都为3，因此3即为27和15的最大公约数。</p>
<p>最小公倍数<br />
两个或多个整数公有的倍数叫做它们的公倍数，其中除0以外最小的一个公倍数就叫做这几个整数的最小公倍数。<br />
求最小公倍数算法：最小公倍数 = 两整数的乘积 ÷ 最大公约数。<br />
请根据以上算法描述编写一段程序，计算并输出两个任意的正整数的最大公约数与最小公倍数。</p>
<p>输入<br />
用空格分开的两个正整数a和b。</p>
<p>输出<br />
输出用空格分开的两个正整数，第一个是最大公约数，第二个是最小公倍数。</p>
<p>输入示例<br />
66 33</p>
<p>输出示例<br />
33 66<br />
下面有两种方法，任选其一即可</p>
<h3 id="辗转相除法"><a class="markdownIt-Anchor" href="#辗转相除法"></a> 辗转相除法</h3>
<figure class="highlight c"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;stdio.h&gt;</span></span></span><br><span class="line"><span class="type">int</span> <span class="title function_">successive</span><span class="params">(<span class="type">int</span> a,<span class="type">int</span> b)</span>&#123;</span><br><span class="line">    <span class="type">int</span> c;</span><br><span class="line">    c=a%b;</span><br><span class="line">    <span class="keyword">if</span>(c==<span class="number">0</span>)</span><br><span class="line">        <span class="keyword">return</span> b;</span><br><span class="line">    <span class="keyword">while</span>(c!=<span class="number">0</span>)&#123;</span><br><span class="line">        a=b;</span><br><span class="line">        b=c;</span><br><span class="line">        c=a%b;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="keyword">return</span> b;</span><br><span class="line">&#125;</span><br><span class="line"><span class="type">int</span> <span class="title function_">main</span><span class="params">()</span>&#123;</span><br><span class="line">    <span class="type">int</span> a,b,multiple,divisor;</span><br><span class="line">    <span class="built_in">scanf</span>(<span class="string">&quot;%d %d&quot;</span>,&amp;a,&amp;b);</span><br><span class="line">    divisor=successive(a,b);</span><br><span class="line">    <span class="built_in">printf</span>(<span class="string">&quot;%d &quot;</span>,divisor);</span><br><span class="line">    multiple=a*b/divisor;</span><br><span class="line">    <span class="built_in">printf</span>(<span class="string">&quot;%d&quot;</span>,multiple);</span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<h3 id="相减法"><a class="markdownIt-Anchor" href="#相减法"></a> 相减法</h3>
<figure class="highlight c"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;stdio.h&gt;</span></span></span><br><span class="line"><span class="type">int</span> <span class="title function_">subtraction</span><span class="params">(<span class="type">int</span> a,<span class="type">int</span> b)</span>&#123;</span><br><span class="line">    <span class="keyword">if</span>(a&gt;b)</span><br><span class="line">        a=a-b;</span><br><span class="line">    <span class="keyword">else</span> <span class="keyword">if</span>(a&lt;b)</span><br><span class="line">        b=b-a;</span><br><span class="line">    <span class="keyword">else</span></span><br><span class="line">        <span class="keyword">return</span> a;</span><br><span class="line">    <span class="keyword">if</span>(a!=b)</span><br><span class="line">        <span class="keyword">return</span> subtraction(a,b);</span><br><span class="line">&#125;</span><br><span class="line"><span class="type">int</span> <span class="title function_">main</span><span class="params">()</span>&#123;</span><br><span class="line">    <span class="type">int</span> a,b,multiple,divisor;</span><br><span class="line">    <span class="built_in">scanf</span>(<span class="string">&quot;%d %d&quot;</span>,&amp;a,&amp;b);</span><br><span class="line">    divisor=subtraction(a,b);</span><br><span class="line">    <span class="built_in">printf</span>(<span class="string">&quot;%d &quot;</span>,divisor);</span><br><span class="line">    multiple=a*b/divisor;</span><br><span class="line">    <span class="built_in">printf</span>(<span class="string">&quot;%d&quot;</span>,multiple);</span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

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